341,338 research outputs found
Imprecise continuous-time Markov chains : efficient computational methods with guaranteed error bounds
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this model. We here improve the uniform approximation method of Krak et al. (2016) in two ways and propose a novel and more efficient adaptive approximation method. For ergodic chains, we also provide a method that allows us to approximate stationary distributions up to any desired maximal error
Material-Specific Investigations of Correlated Electron Systems
We present the results of numerical studies for selected materials with
strongly correlated electrons using a combination of the local-density
approximation and dynamical mean-field theory (DMFT). For the solution of the
DMFT equations a continuous-time quantum Monte-Carlo algorithm was employed.
All simulations were performed on the supercomputer HLRB II at the Leibniz
Rechenzentrum in Munich. Specifically we have analyzed the pressure induced
metal-insulator transitions in Fe2O3 and NiS2, the charge susceptibility of the
fluctuating-valence elemental metal Yb, and the spectral properties of a
covalent band-insulator model which includes local electronic correlations.Comment: 14 pages, 7 figures, to appear in "High Performance Computing in
Science and Engineering, Garching 2009" (Springer
Mean field analysis for Continuous Time Bayesian Networks
In this paper we investigate the use of the mean field technique to analyze Continuous Time Bayesian Networks (CTBN). They model continuous time evolving variables with exponentially distributed transition rates depending on the parent variables in the graph. CTBN inference consists of computing the probability distribution of a subset of variables, conditioned by the observation of other variables' values (evidence). The computation of exact results is often unfeasible due to the complexity of the model. For such reason, the possibility to perform the CTBN inference through the equivalent Generalized Stochastic Petri
Net (GSPN) was investigated in the past. In this paper instead, we explore the use of mean field approximation and apply it to a well-known epidemic case study. The CTBN model is converted in both a GSPN and in a mean field based model. The example is then analyzed with both solutions, in order to evaluate the accuracy of the mean field approximation for the computation of the posterior probability of the CTBN given an evidence. A summary of the lessons learned during this preliminary attempt concludes the paper
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General optimized lower and upper bounds for discrete and continuous arithmetic Asian options
We propose an accurate method for pricing arithmetic Asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation. In particular, we derive analytical expressions for the lower bound in the Fourier domain. This is then recovered by a single univariate inversion and sharpened using an optimization technique. In addition, we derive an upper bound to the error from the lower bound price approximation. Our proposed method can be applied to computing the prices and price sensitivities of Asian options with fixed or floating strike price, discrete or continuous averaging, under a wide range of stochastic dynamic models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. Our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases
Parallel Rollout for Deterministic Optimal Control
We extend the parallel rollout algorithm for solving deterministic infinite
horizon optimal control problems with nonnegative stage costs. Given the exact
or approximate cost functions of several base policies, the proposed scheme can
harness the presence of multiple computing units. We show that the proposed
scheme permits a parallel implementation, and can be viewed as a decomposition
method for solving challenging optimization problems that arise in model
predictive control (MPC) or related approximation schemes. When applied to
problems involving continuous state and control spaces, our method requires
computing multiple copies of similar MPC problems with common dynamics and
stage costs
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